Algebra 2 Warm Up Mar. 11, 2014
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1 Algera Warm Up Mar., Name:. A floor tile is made up of smaller squares. Each square measures i. o each side. Fid the perimeter of the floor tile.. A sectio of mosaic tile wall has the desig show at the right. The desig is made up of equilateral triagles. Each side of the large triagle is i. ad each side of a small triagle is i. Fid the total area of the desig to the earest teth of a ich.
2 Algera Ratioal Expoets Name: Ratioal Expoets ad Radicals (th Roots) Notatio: There are two ways to write a expressio for the th root of a umer. We already leared to use the radical otatio: 7 meas the rd root of 7. Aother way to express this idea is to use ratioal expoets. Recall that a ratioal umer ca e writte as a fractio made of two itegers. So a ratioal expoet is just a expoet i fractio form. The expoet for the th root of a umer is. Example: 7 ca e writte as 7 ad i oth cases they represet the umer. Whe we use ratioal expoets, the deomiator represets the root ad the umerator represets the power. Examples: a) = ) c) 8 8 d) 6 e) 6 6 You ca rewrite expressios from oe form to the other to make simplifyig easier. Ratioal expoets follow the same properties as iteger expoets, so that is a coveiet way to multiply radicals that have differet roots. Examples: What is the simplified form of each expressio? a Use 6 Add. 6 Use m m a a a. 6 Simplify. x x.. Write (6 x )( x ) i simplified form. (6 x )( x ) 6x x m m+ 6x x Use x x x. 7 x Simplify.
3 Exercises Simplify each expressio. Assume that all variales are positive ( y )( y ). ( ) ( ) ( ). 5 y y ( x )(7 x )
4 Name: Date: Algera : Guidelies for Applyig Properties of Expoets Products Quotiets Bases are the same Add the expoets: m m Sutract the expoets: m m (order matters!) Expoets are the same Multiply the ases: a a a Divide the ases: a Power of a Power Multiply the expoets: m m a a Except for zero itself, ay real umer raised to the zero power is oe: Zero Power ( is udefied) Negative Expoet The egative expoet meas oe over the positive power: ad Example with a factor that is ot expoetiated: a a a ad a Rewritig Radicals The root is the deomiator ad the power is the umerator:
5 Name Class Date 6- Practice Form G Simplify each expressio.. Ratioal Expoets ( 5) ( 5) ( 5) Write each expressio i radical form.. x m.. Write each expressio i expoetial form. ( ) y 5. z 8. 7 t..5 a ( a ) a.6. x. m. 5y 5. y 6. ( ) (6 a ) (5 a ). The rate of iflatio i that raises the cost of a item from the preset value P to F t the future value F over t years is foud usig the formula i. P Roud your aswers to the earest teth of a percet. a. What is the rate of iflatio for which a televisio set costig $ today will ecome oe costig $5 i years?. What is the rate of iflatio that will result i the price P doulig (that is, F = P) i years? Pretice Hall Gold Algera Teachig Resources Copyright y Pearso Educatio, Ic., or its affiliates. All Rights Reserved.
6 Name Class Date 6- Practice (cotiued) Form G Ratioal Expoets Write each expressio i simplest form. Assume that all variales are positive.. 5. (8 ) ( ) (56 ) ( 7) 8. x x 9. y y. (8 ) ( x )( x ) 6. y y 7. ( a ) 8. 9 ( y ) 9. 6 ( a ) 5. y 5 8 y 5. x x 7 5. ( a ) ( x )(6 x ) 55. xy (9 ) 56. 7x 6y x y x y 58. y 5 8 y 59. x y 6 x x x 6. x y x 6. 75y 6. I a test kitche, researchers have measured the radius of a all of dough made with a ew quick-actig yeast. Based o their data, the radius r of the dough all, i cetimeters, is give y r 5(.5) t after t miutes. Roud the aswers to the followig questios to the earest teth of a cm. a. What is the radius after 5 miutes?. What is the radius after miutes? c. What is the radius after miutes? 8 Pretice Hall Gold Algera Teachig Resources Copyright y Pearso Educatio, Ic., or its affiliates. All Rights Reserved.
= 4 and 4 is the principal cube root of 64.
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